Quantum-mechanically, waves and particles are one and the same. What exactly do you mean?

Is it that when photons (when considered as particles) are absorbed by electron...then the electrons should be described a particle.....and that when photons are considered as waves the electron, absorbing it is also wave......my question was can we consider electrons as waves while considering the photon, that the electron absorbs, as particles.....how would you describe a wave absorbing a particle......

With great difficulty. Because photons are being destroyed, regular quantum mechanics won't work, and you have to use quantum field theory to do it properly. Dirac was the first person to work it out in a famous paper around the middle of the century.

As far as I can remember from my quantum mechanics classes to properly describe it you need to do things like qunatise the radiation field and use destruction and creation operators. It's fairly standard in quantum field theory I think. Probably the best way of looking at this particle wave thing is to realise that both descriptions are correct at the same time. Essentially though when you deal with this stuff you just end up using the wave-functions to do the hard number crunching.